Electronic Journal of Statistics

Bayesian inference with rescaled Gaussian process priors

Aad van der Vaart and Harry van Zanten

Full-text: Open access

Abstract

We use rescaled Gaussian processes as prior models for functional parameters in nonparametric statistical models. We show how the rate of contraction of the posterior distributions depends on the scaling factor. In particular, we exhibit rescaled Gaussian process priors yielding posteriors that contract around the true parameter at optimal convergence rates. To derive our results we establish bounds on small deviation probabilities for smooth stationary Gaussian processes.

Article information

Source
Electron. J. Statist. Volume 1 (2007), 433-448.

Dates
First available in Project Euclid: 22 October 2007

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1193074818

Digital Object Identifier
doi:10.1214/07-EJS098

Mathematical Reviews number (MathSciNet)
MR2357712

Zentralblatt MATH identifier
1140.62066

Subjects
Primary: 62G05: Estimation 62C10: Bayesian problems; characterization of Bayes procedures
Secondary: 60G15: Gaussian processes

Keywords
Rate of convergence Bayesian inference nonparametric density estimation nonparametric regression classification Gaussian process priors

Citation

van der Vaart, Aad; van Zanten, Harry. Bayesian inference with rescaled Gaussian process priors. Electron. J. Statist. 1 (2007), 433--448. doi:10.1214/07-EJS098. https://projecteuclid.org/euclid.ejs/1193074818


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